Free Sequentially in Orthogonal Order-Sorted Rewriting Systems with Constructors

We introduce the notions of sequentiality and strong sequentiality in order-sorted rewriting systems, both closely related to the subsort order and to the form of declarations of the signature. We deene free sequentiality for the class of orthogonal systems with constructors, a notion which does not impose conditions over the signature. We provide an eeective decision procedure for free sequentiality that gives at the same time a simple construction of a non-deterministic pattern matching tree. These trees describe how the reenement of sorts and structures has to be done along the reduction sequence in such a way that wasteful computations are avoided.